CN115265750A - Optical fiber distributed acoustic wave sensing system and method - Google Patents

Optical fiber distributed acoustic wave sensing system and method Download PDF

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CN115265750A
CN115265750A CN202210852392.9A CN202210852392A CN115265750A CN 115265750 A CN115265750 A CN 115265750A CN 202210852392 A CN202210852392 A CN 202210852392A CN 115265750 A CN115265750 A CN 115265750A
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acoustic wave
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wave sensing
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CN115265750B (en
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吴杰
黄山石
陈继宣
郑晓周
杨立委
何鹏程
朱莉
齐晓东
李以
林国伟
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Wenzhou Institute Of Quality Technology Testing
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Abstract

The invention discloses an optical fiber distributed acoustic wave sensing system and method, and belongs to the technical field of optical fiber distributed acoustic wave sensing systems. The optical fiber distributed acoustic wave sensing system comprises a machine learning algorithm of morphological feature extraction and joint analysis, wherein a microstructure optical fiber detection system can obtain a large amount of high-precision signal data, and a large amount of data samples are provided as a support of an identification basis. In order to solve the problem that coherent fading can be improved to a certain extent by adopting a multi-phase and frequency method, but coherent fading of Rayleigh scattering signals cannot be eliminated essentially, an optical phase modulation technology is adopted, and a laser low-frequency phase noise suppression technology and a wavelet decomposition signal noise reduction algorithm are combined to realize accurate measurement of slowly varying acoustic signals, so that the bottleneck of slowly varying weak acoustic signal detection in the traditional technology is broken through.

Description

Optical fiber distributed acoustic wave sensing system and method
Technical Field
The invention relates to the technical field of optical fiber distributed acoustic wave sensing systems, in particular to an optical fiber distributed acoustic wave sensing system and method.
Background
The acoustic wave is widely present in all aspects of human activities in human society, has high penetration and long-distance transmission characteristics, and can realize target positioning and anomaly analysis through detection of acoustic wave information. At present, the precision measurement based on sound wave detection is widely applied to a plurality of fields, including the field of geophysical detection, and can realize oil well exploration and geological imaging; in the field of large-scale engineering, the monitoring of tunnel structure and track health can be realized; in the military field, a hydrophone array, an intelligent skin and a sound wave warning fence can be realized; in the field of energy transmission, pipe network state monitoring, corrosion early warning and the like can be realized; in the medical field, the perspective imaging, the online diagnosis and the like of body organs are realized. The sound wave detection has wide and important utilization value.
The existing acoustic wave detection instruments are various in types, the existing common electrical acoustic wave sensors can be divided into a resistance conversion type, an electromagnetic conversion type and a capacitance conversion type, due to the fact that the existing acoustic wave detection instruments comprise circuit structures, the existing electrical acoustic wave sensors cannot be used in application scenes such as the field, the existing acoustic wave detection instruments are usually single-point detection, and the detection frequency range is limited.
1) The prior art still has difficulty in realizing high-precision measurement of distributed infrasonic waves
2) Coherent fading can be improved to a certain extent by adopting a multi-phase and frequency method, but the coherent fading of Rayleigh scattering signals cannot be eliminated essentially; therefore, the existing requirements are not met, and a fiber-optic distributed acoustic wave sensing system and a method are provided for the same.
Disclosure of Invention
The invention aims to provide an optical fiber distributed acoustic wave sensing system and method, which adopt an optical phase modulation technology, combine a laser low-frequency phase noise suppression technology and a wavelet decomposition signal denoising algorithm, and realize accurate measurement of slowly varying acoustic signals, thereby breaking through the bottleneck of slowly varying weak acoustic wave signal detection in the traditional technology and solving the problems in the prior art.
In order to achieve the purpose, the invention provides the following technical scheme: the optical fiber distributed acoustic wave sensing system comprises a machine learning algorithm of morphological feature extraction and joint analysis, wherein a microstructure optical fiber detection system can obtain a large amount of high-precision signal data, and a large amount of data samples are provided as supports of identification bases.
The neural network has excellent capability of constructing nonlinear mapping and is adjusted into a proper mapping network through a large enough number of data samples;
combining the collected data to form a time and space multi-dimensional image, preprocessing the image and then sending the image into a neural network for learning;
the method comprises the steps that characteristic details of the form of a data sample are searched by disassembling an image, the data sample is compared with an actual result at a terminal when being sent to a neural network for learning, an error function corrects the network according to the results, and finally a proper model is constructed through the learning and verification of mass data;
marking a large amount of data of different types, removing unnecessary information based on a data cleaning method, and training by adopting a time and space combined image;
aiming at abnormal points possibly existing in training data, and the abnormal points cannot be identified and eliminated in the data cleaning process, the overfitting phenomenon is reduced by introducing a residual error neural network to remove useless ganglia, the performance is further improved on the basis of the original network, and the complexity of the network is reduced.
Preferably, the microstructure optical fiber detection system adopts a neural network to perform signal identification, performs joint analysis on signals with multiple dimensions of time and space, extracts morphological characteristics of signal images, and realizes high-precision target intelligent identification and positioning through training of a large number of data samples.
Preferably, the convolutional neural network comprises a convolutional layer for extracting features, a pooling layer for compressing features and a full-link layer for adjusting output forms;
the method comprises the steps of extracting images by utilizing convolution kernels in the convolutional layer, performing similar feature marking on morphology, performing network calculation on data with labels and judgment data images, comparing error functions with data labels, adjusting parameters of the convolutional layer according to the output of the error functions, and achieving intelligent identification of detection signals.
Preferably, the stress and the fiber running speed are controllable by improving the optical fiber looping process technology.
Preferably, parameters such as single pulse energy of the ultraviolet pulse laser, fiber running speed of the optical fiber and the like are optimized.
Preferably, the direct writing process for detecting the microstructure units on line in real time is realized by combining the template automatic control technology and the optical time domain reflection method, and the longitudinally distributed microstructure sensing optical fiber with multiple measuring points, low loss, uniform and controllable strength and controllable spatial distribution is realized.
Preferably, the distributed phase demodulation method based on the optical fiber distributed acoustic wave sensing system includes the following steps:
the signal-to-noise ratio is improved by adopting a laser coherent detection technology, and the signal-to-noise ratio of the beat frequency signal is improved by coherent detection through local oscillator light;
carrying out phase analysis by adopting an IQ demodulation technology on communication to obtain real-time high-fidelity phase recovery, wherein common-mode noise of a light source and a link is eliminated by adopting a self-reference phase extraction method between an nth microstructure point and an n-1 st microstructure point;
obtaining distributed phase distribution along the optical fiber by combining an optical time domain reflection technology;
determining the starting time of each scattering sequence through a clock locking and cross-correlation phase demodulation algorithm, distinguishing injected light pulse scattering signals of different time slots, and realizing the improvement of the distance band-width product of distributed sensing;
the effective sensing optical signal is represented in an independent pulse form in a time domain, the time between pulses is called a time slot, and if scattering points are arranged on the optical fiber at uniform intervals and the time slot between adjacent scattering points is larger than the width of the optical pulse, further time slot multiplexing can be carried out on the backscattered light signals.
Preferably, the optical fiber system completes coherent beat frequency detection of laser signals output by the fiber laser based on the short-cavity DBR and the dual-wavelength annular-cavity fiber laser in sequence, and realizes high-precision measurement of torsional deformation, earthquake inclination and micro-vibration and online monitoring of human pulse and respiration;
the coherent detection technology is combined with the microstructure sensing optical fiber, the project group realizes the full-distribution dynamic strain measurement of 4m spatial resolution at the distance of 1.3km, and can respond to the frequency band of 2Hz-5 kHz.
Preferably, the signals demodulated by the optical fiber system are uploaded to a PC (personal computer) terminal in real time through an RS232 network port by a TCP/IP (transmission control protocol/Internet protocol), and sound wave detection application software is autonomously developed on the PC, and has the functions of distributed monitoring result display, real-time abnormity alarm, data recording and storage and the like, such as initialization setting, data receiving, feature extraction, mode identification, event classification and early warning and the like.
Preferably, the method for suppressing low-frequency noise based on the optical fiber distributed acoustic wave sensing system includes the following steps:
by extracting low-frequency noise information of units in an area where an abnormal signal source is located, aiming at the characteristics that the effect of temperature on the optical cable is long-term stable and the low-frequency noise changes randomly, a self-adaptive filtering algorithm is adopted;
analyzing the obtained low-frequency noise source channel signal and the channel signal of the high-temperature abnormal area by using a plurality of sensors;
and optimizing parameters of the adaptive filter by using an LMS algorithm to ensure that the filtered signal in the noise source channel is linearly consistent with the noise component in the signal source channel.
Compared with the prior art, the invention has the beneficial effects that:
1. according to the sensing demodulation method based on time slot multiplexing, time slot redundancy among micro-structure optical fiber back scattering signals is utilized, the response frequency band of sound wave detection is expanded through a pulse multiplexing technology, and the technical bottleneck in long-distance sound wave detection is broken through;
2. according to the invention, aiming at interference fading generated by interference cancellation of different Rayleigh scattering points in the pulse width, the strength of a backward sensing signal at a fading position is close to zero and submerged in noise, so that a vibration signal phase demodulation error is caused, and the accuracy of signal perception is seriously influenced, only one enhanced microstructure scattering signal is stored in the pulse width of the scattering enhanced microstructure sensing optical fiber, so that the random coherent fading of the backward sensing signal is fundamentally solved;
3. in the invention, for realizing the perception of weak slowly-changed sound wave signals, the detection sensitivity and reliability of sensing need to be improved, and for the phase modulation type optical fiber perception technology, the low-frequency phase noise has great influence, so that the problem of low-frequency noise suppression needs to be solved;
4. according to the invention, effective sensing optical signals are represented in an independent pulse form in a time domain, time between pulses is called a time slot, if scattering points are uniformly arranged on an optical fiber at intervals, and the time slot between adjacent scattering points is larger than the width of an optical pulse, further time slot multiplexing can be carried out on backscattered light signals, when a plurality of sequences of backscattered light pulse signals coexist in the time slot, the effective optical signals keep mutually independent relation, so that the sensing demodulation can still be realized by using a cross-correlation phase demodulation algorithm after superposition, the high-frequency response of a system is improved, when the optical pulse transmitting frequency of the system is n +1 times of a fundamental frequency f, more optical pulses are inserted into the time slot, the system can respond to the highest frequency and improve n times, and the limitation of the length of the optical fiber on a response frequency band is overcome;
5. according to the invention, parameters of the adaptive filter are optimized by using an LMS algorithm, so that a filtered signal in a noise source channel is linearly consistent with a noise component in a signal source channel, and since the noise elimination algorithm is used for filtering noise and then eliminating the noise by using a signal source to obtain a final signal, slowly changing information of a low-frequency sound wave signal is retained to the maximum extent, so that the system is sensitive and accurate to the change of an external environment, and finally, the characteristic of high positioning precision of a distributed sensor is combined to realize high-sensitivity and high-precision small-scale high-temperature anomaly monitoring.
Drawings
FIG. 1 is a block diagram of an acoustic wave sensing architecture of the present invention;
FIG. 2 is a diagram of a residual neural network architecture of the present invention;
FIG. 3 is a schematic diagram of the phase demodulation process of the present invention;
FIG. 4 is a schematic diagram of a slot reuse scheme of the present invention;
FIG. 5 is a chart of demodulation test wave frequencies of the present invention;
fig. 6 is a flow chart of the low frequency noise suppression according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1-2, an embodiment of the present invention is shown: the optical fiber distributed acoustic wave sensing system comprises a machine learning algorithm of morphological feature extraction and joint analysis, wherein a microstructure optical fiber detection system can acquire a large amount of high-precision signal data and provides a support for a large amount of data samples as an identification basis.
The neural network has excellent capability of constructing nonlinear mapping and is adjusted into a proper mapping network through a large enough number of data samples;
combining the collected data to form a time and space multi-dimensional image, preprocessing the image and then sending the image into a neural network for learning, wherein the characteristic details of the image in the aspect of form are searched by disassembling the image, when the data sample is sent into the neural network for learning, the data sample is compared with an actual result at a terminal, an error function corrects the network according to the results, and finally a proper model is constructed through the learning and verification of mass data;
marking a large amount of different types of data, removing unnecessary information based on a data cleaning method, and training by adopting a time and space combined image;
aiming at abnormal points possibly existing in training data and incapability of being identified and eliminated in the data cleaning process, the overfitting phenomenon is reduced by introducing a residual error neural network to remove useless ganglia, the performance is further improved on the basis of the original network, and the network complexity is reduced.
The microstructure optical fiber detection system adopts a neural network to carry out signal identification, carries out joint analysis on signals with multiple dimensions of time and space, extracts morphological characteristics of signal images, and realizes high-precision target intelligent identification and positioning through training of a large number of data samples.
The convolutional neural network comprises a convolutional layer for extracting characteristics, a pooling layer for compressing characteristics and a full-connection layer for adjusting an output form, wherein images can be extracted by utilizing convolutional kernels in the convolutional layer, similar characteristic labeling is carried out morphologically, network calculation is carried out on data with labels and judgment data images, comparison is carried out on the data with the labels through error functions, parameters of the convolutional layer are adjusted according to the output of the error functions, and intelligent identification of detection signals is realized;
the microstructure-based optical fiber distributed sound wave detection system has the advantages of passive detection, no electromagnetic interference and stable work in severe environment, meanwhile, the optical fiber distributed sound wave detection technology has the advantages of easiness in installation, easiness in networking, long distance, high sensitivity, large dynamic range and the like, multiple sound wave signals can be accurately monitored by only one system and one optical cable, long-distance distributed online monitoring is achieved, the application value is remarkable in multiple fields, and the microstructure-based optical fiber distributed sound wave detection system has remarkable advancement.
The stress and the fiber running speed are controllable by improving an optical fiber winding process technology, the direct writing process for detecting the microstructure units on line in real time is realized by optimizing parameters such as single pulse energy of an ultraviolet pulse laser, the fiber running speed of the optical fiber and the like, and the longitudinal distribution microstructure sensing optical fiber with multiple measuring points, low loss, uniform and controllable intensity and controllable spatial distribution is realized by combining a template automatic control technology and an optical time domain reflection method.
Referring to fig. 3-5, the distributed phase demodulation method based on the optical fiber distributed acoustic wave sensing system includes the following steps:
the signal-to-noise ratio is improved by adopting a laser coherent detection technology, and the signal-to-noise ratio of the beat frequency signal is improved by coherent detection through local oscillator light;
carrying out phase analysis by adopting an IQ demodulation technology on communication to obtain real-time high-fidelity phase recovery, wherein common-mode noise of a light source and a link is eliminated by adopting a self-reference phase extraction method between an nth microstructure point and an n-1 st microstructure point;
the distributed phase distribution along the optical fiber is obtained by combining an optical time domain reflection technology, the initial time of each scattering sequence is determined by a clock locking and cross-correlation phase demodulation algorithm, the injected optical pulse scattering signals in different time slots are distinguished, and the improvement of the distance band-width product of distributed sensing is realized;
effective sensing optical signals are represented in an independent pulse form in a time domain, time between pulses is called a time slot, if scattering points are arranged on an optical fiber at uniform intervals, and the time slot between adjacent scattering points is larger than the width of an optical pulse, further time slot multiplexing can be carried out on backscattered light signals, when a plurality of sequences of backscattered light pulse signals coexist in the time slot, the effective optical signals keep mutually independent relation, therefore, after superposition, the cross-correlation phase demodulation algorithm can still be used for realizing sensing demodulation, so that the high-frequency response of a system is improved, when the emission frequency of the system optical pulse is n +1 times of a fundamental frequency f, more optical pulses are inserted into the time slot, the system can respond to the highest frequency and improve n times, and therefore, the limitation of the length of the optical fiber on a response frequency band is overcome.
The optical fiber system completes coherent beat frequency detection of laser signals output by the fiber laser based on the short-cavity DBR and the dual-wavelength annular cavity fiber laser in sequence, and realizes high-precision measurement of torsional deformation, earthquake inclination and micro-vibration and online monitoring of human body pulse and respiration;
the coherent detection technology is combined with the microstructure sensing optical fiber, the project group realizes the full-distribution dynamic strain measurement of 4m spatial resolution at the distance of 1.3km, and can respond to the frequency band of 2Hz-5 kHz.
The signals demodulated by the optical fiber system are uploaded to a PC (personal computer) terminal in real time through an RS232 network port by a TCP/IP (transmission control protocol/Internet protocol) protocol, and sound wave detection application software is autonomously developed on the PC, and the functions of initialization setting, data receiving, feature extraction, mode identification, event classification, early warning and other functions of distributed monitoring result display, real-time abnormal alarm, data recording, storage and the like are included.
Referring to fig. 6, the method for suppressing low-frequency noise based on the optical fiber distributed acoustic wave sensing system includes the following steps:
by utilizing the advantage of full coverage of a distributed sensor area and the characteristic that a low-frequency noise background has the same effect on a plurality of sensors in the same area, a self-adaptive filtering algorithm is adopted aiming at the characteristics that the effect of temperature on an optical cable is long-term stable and the low-frequency noise changes randomly by extracting low-frequency noise information of a plurality of units in the area where an abnormal signal source is located;
analyzing the obtained low-frequency noise source channel signal and the channel signal of the high-temperature abnormal area by using a plurality of sensors;
the parameters of the adaptive filter are optimized by using an LMS algorithm, so that the filtered signals in a noise source channel are linearly consistent with the noise components in a signal source channel, the noise elimination algorithm is used for filtering noise, then the signal source is used for eliminating the noise to obtain final signals, the slowly changing information of low-frequency sound wave signals is kept to the maximum extent, the system is sensitive and accurate to the change of the external environment, and finally the characteristic of high positioning precision of a distributed sensor is combined to realize high-sensitivity and high-precision small-scale high-temperature anomaly monitoring.
In combination, the microstructure optical fiber detection system can acquire a large amount of high-precision signal data and provides a support for taking a large amount of data samples as identification bases. The neural network is adopted for signal recognition, joint analysis is carried out on time-space multi-dimensional signals, morphological characteristics of signal images are extracted, high-precision target intelligent recognition and positioning are achieved through training of a large number of data samples, the neural network has excellent capacity of constructing nonlinear mapping, and the neural network is adjusted into a proper mapping network through a large enough number of data samples. The single channel signal contains limited information, cannot reflect the difference of different points on the space distance, and lacks key dimension information. And combining the acquired data to form a time-space multi-dimensional image, preprocessing the image and then sending the preprocessed image to a neural network for learning. The project selects a convolutional neural network, the characteristic details in the aspect of the form of the convolutional neural network are searched by disassembling images, when a data sample is sent to the neural network for learning, the data sample is compared with an actual result at a terminal, an error function corrects the network according to the results, and finally a proper model is constructed through the learning and verification of mass data, wherein the convolutional neural network comprises a convolutional layer for extracting the characteristics, a pooling layer for compressing the characteristics and a full connection layer for adjusting the output form. Images can be extracted by using convolution kernels in the convolution layer, and similar feature labeling is carried out on morphology. And carrying out network calculation on the data with the label and the judgment data image, comparing the data with the judgment data image through an error function, adjusting the parameter of the convolution layer according to the output of the error function, realizing intelligent identification of detection signals, marking a large number of different types of data, removing unnecessary information based on a data cleaning method, and training by adopting a time-space combined image. Aiming at abnormal points possibly existing in training data and incapability of being identified and eliminated in the data cleaning process, a residual error neural network is introduced in the project, the overfitting phenomenon is reduced by removing useless ganglia, the performance is further improved on the basis of the original network, and the network complexity is reduced. And finally realizing the multi-task identification and positioning network through multiple iterations and tests.
It should be noted that, in this document, relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (7)

1. An optical fiber distributed acoustic wave sensing system is characterized by comprising a machine learning algorithm of morphological feature extraction and joint analysis, wherein a microstructure optical fiber detection system can acquire a large amount of high-precision signal data and provide a data sample as a support for identification basis,
adjusting the data sample into a proper mapping network;
combining the collected data to form a time and space multi-dimensional image, preprocessing the image and then sending the image into a neural network for learning;
the method comprises the steps that characteristic details of the form of a data sample are searched by disassembling an image, the data sample is compared with an actual result at a terminal when being sent to a neural network for learning, an error function corrects the network according to the results, and finally a proper model is constructed through the learning and verification of mass data;
marking a large amount of different types of data, removing unnecessary information based on a data cleaning method, and training by adopting a time and space combined image;
aiming at abnormal points possibly existing in training data and incapability of being identified and eliminated in the data cleaning process, the overfitting phenomenon is reduced by introducing a residual error neural network to remove useless ganglia.
2. A fiber optic distributed acoustic wave sensing system according to claim 1, wherein: the microstructure optical fiber detection system adopts a neural network to carry out signal identification, carries out joint analysis on signals with multiple dimensions of time and space, and extracts morphological characteristics of signal images.
3. A fiber optic distributed acoustic wave sensing system according to claim 1, wherein: the convolutional neural network comprises a convolutional layer for extracting characteristics, a pooling layer for compressing characteristics and a full-connection layer for adjusting an output form;
the method comprises the steps of extracting images by utilizing convolution kernels in the convolutional layer, performing similar feature marking on morphology, performing network calculation on data with labels and judgment data images, comparing error functions with data labels, adjusting parameters of the convolutional layer according to the output of the error functions, and achieving intelligent identification of detection signals.
4. The optical fiber distributed acoustic wave sensing system according to claim 1, wherein the distributed phase demodulation method based on the optical fiber distributed acoustic wave sensing system comprises the following steps:
the signal-to-noise ratio is improved by adopting laser coherent detection, and the signal-to-noise ratio of a detection beat frequency signal is improved by coherent detection through local oscillator light;
carrying out phase analysis by adopting IQ demodulation to obtain real-time high-fidelity phase recovery, wherein common mode noise of a light source and a link is eliminated by adopting a self-reference phase extraction method between the nth and the (n-1) th microstructure points;
combining optical time domain reflection to obtain distributed phase distribution along the optical fiber;
determining the starting time of each scattering sequence through a clock locking and cross-correlation phase demodulation algorithm, distinguishing injected light pulse scattering signals of different time slots, and realizing the improvement of the distance band-width product of distributed sensing;
the effective sensing optical signal is represented in an independent pulse form in a time domain, the time between pulses is called a time slot, and if scattering points are arranged on the optical fiber at uniform intervals and the time slot between adjacent scattering points is larger than the width of the optical pulse, further time slot multiplexing can be carried out on the backscattered light signals.
5. The distributed phase demodulation method based on the optical fiber distributed acoustic wave sensing system according to claim 4, wherein: the optical fiber system is based on coherent beat frequency detection of laser signals output by a short-cavity DBR optical fiber laser and a dual-wavelength annular cavity optical fiber laser, and realizes high-precision measurement of torsional deformation, earthquake inclination and micro-vibration and online monitoring of human body pulse and respiration.
6. The distributed phase demodulation method based on the optical fiber distributed acoustic wave sensing system according to claim 5, wherein: the signals demodulated by the optical fiber system are uploaded to a PC (personal computer) terminal in real time through an RS232 network port by a TCP/IP (transmission control protocol/Internet protocol), and sound wave detection application software is autonomously developed on the PC, and the functions of initialization setting, data receiving, feature extraction, mode identification, event classification, early warning and other distributed monitoring result display, real-time abnormity alarm, data recording and storage are realized.
7. The optical fiber distributed acoustic wave sensing system according to claim 1, wherein the method for suppressing low-frequency noise based on the optical fiber distributed acoustic wave sensing system comprises the following steps:
extracting low-frequency noise information of a unit passing through the area where the abnormal signal source is located, and adopting a self-adaptive filtering algorithm;
analyzing the obtained low-frequency noise source channel signal and the channel signal of the high-temperature abnormal area by using a plurality of sensors;
and optimizing parameters of the adaptive filter by using an LMS algorithm to ensure that the filtered signal in the noise source channel is linearly consistent with the noise component in the signal source channel.
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